This invention relates to adiabatic power conversion, and in particular to configuration and control for partial adiabatic operation of a charge pump.
Various configurations of charge pumps, including Series-Parallel and Dickson configurations, rely on alternating configurations of switch elements to propagate charge and transfer energy between the terminals of the charge pump. Energy losses associated with charge propagation determine the efficiency of the converter.
Referring to FIG. 1, a single-phase Dickson charge pump 100 is illustrated in a step-down mode coupled to a low-voltage load 110 and a high-voltage source 190. In the illustrated configuration, generally the low-voltage load 110 is driven (on average) by a voltage that is ⅕ times the voltage provided by the source and a current that is five times the current provided by the high-voltage source 190. The pump is driven in alternating states, referred to as state one and state two, such that the switches illustrated in FIG. 1 are closed in the indicated states. In general, the duration of each state is half of a cycle time T and the corresponding switching frequency of the charge pump 100 is equal to the inverse of the cycle time T.
FIGS. 2A-B illustrate the equivalent circuit in each of states two and state one, respectively, illustrating each closed switch as an equivalent resistance R. Capacitors C1 through C4 have a capacitance C. In a first conventional operation of the charge pump 100, the high-voltage source 190 is a voltage source, for example, a twenty-five volt source, such that the low-voltage load 100 is driven by five volts. In operation, the voltage across the capacitors C1 through C4 are approximately five volts, ten volts, fifteen volts, and twenty volts, respectively.
One cause of energy loss in the charge pump 100 relates the resistive losses through the switches (i.e., through the resistors R in FIGS. 2A-B). Referring to FIG. 2A, during state two, charge transfers from the capacitor C2 to the capacitor C1 and from the capacitor C4 to the capacitor C1. The voltages on these pairs of capacitors equilibrate assuming that the cycle time T is sufficiently greater than the time constant of the circuit (e.g., that the resistances R are sufficiently small. Generally, the resistive energy losses in this equilibration are proportional to the time average of the square of the current passing between the capacitors and therefore passing to the low-voltage load 110. Similarly, during state one, the capacitors C3 and C2 equilibrate, the capacitor C4 charges, and the capacitor C1 discharges, also generally resulting in a resistive energy loss that is proportional to the time average of the square of the current passing to the low-voltage load 110.
For a particular average current passing to the load 110, assuming that the load presents an approximately constant voltage, it can be shown than the resistive energy loss decreases as the cycle time T is reduced (i.e., switching frequency is increased). This can generally be understood by considering the impact of dividing the cycle time by one-half, which generally reduces the peak currents in the equilibration by one half, and thereby approximately reduces the resistive energy loss to one quarter. So the resistive energy loss is approximately inversely proportional to the square of the switching frequency.
However, another source of energy loss relates to capacitive losses in the switches, such that energy loss grows with the switching frequency. Generally, a fixed amount of charge is lost with each cycle transition, which can be considered to form a current that is proportional to the switching frequency. So this capacitive energy loss is approximately proportional to the square of the switching frequency.
Therefore, with a voltage source and load there an optimal switching frequency that minimizes the sum of the resistive and capacitive energy losses, respectively reduced with increased frequency and increased with increased frequency.